Let X be a random variable representing the n | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The sample space $S$ for tossing three fair coins is given by: $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$. The total number of outcomes is $

Vedclass · Accepted Answer

$\frac{3}{8}$

Vedclass · Answer

(A) The sample space $S$ for tossing three fair coins is given by: $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$. The total number of outcomes is $n(S) = 8$. $X$ is a random variable representing the number of heads. We need to find $P(X = 2)$,which is the probability of getting exactly two heads. The outcomes with exactly two heads are $\{HHT, HTH, THH\}$. Thus,the number of favorable outcomes is $n(X = 2) = 3$. Therefore,$P(X = 2) = \frac{n(X = 2)}{n(S)} = \frac{3}{8}$.

Let $X$ be a random variable representing the number of heads obtained when three fair coins are tossed simultaneously. Find the value of $P(X = 2)$.

Similar Questions

If $X$ is a Poisson variate such that $P(X=1) = 2P(X=2)$,then $P(X=3)$ is equal to:

If the mean of a Poisson variate $X$ is $1$,then $\sum_{r=0}^{\infty}|r-1| P(X=r)=$

In a Poisson distribution, if $\frac{P(X=5)}{P(X=2)}=\frac{1}{7500}$ and $\frac{P(X=5)}{P(X=3)}=\frac{1}{500}$, then the mean of the distribution is

$A$ random variable $X$ has the following probability distribution:
$X$: $1, 2, 3, 4$
$P(X)$: $0.2, 0.4, 0.3, 0.1$
The mean and variance of $X$ are respectively:

On an average,if one out of $100$ electric bulbs produced by a company is found to be defective,then the probability that there are at least two defective bulbs in a consignment of $600$ bulbs is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module